The Complete Engineering Mechanics Course

Master vector operations by applying parallelogram and triangle laws to find resultant of two forces from the same point. Use opposite, adjacent, and hypotenuse with sine rules in triangles.

Compute forces A and B and the Fita for an 888 N resultant along the x axis using parallelogram and triangle methods with 40 and 50 degree angles.

Apply vector operations to solve a three-force problem using triangle and parallelogram methods to minimize the third cable force while achieving a 400 N resultant, then compute theta and F.

explains algebraic vector addition with rectangular components in a plane, using i and j unit vectors to combine forces along x and y, with a three-force example.

Explore algebraic vector addition by resolving forces into cartesian components, solving for unknowns with sine and cosine, and determining the resultant's magnitude and direction.

Explore Cartesian vectors in three dimensions by expressing a force as x, y, and z components and calculating magnitude and direction using unit vectors and angles alpha, beta, and gamma.

Learn to compute the resultant force of two forces in three dimensions by constructing Cartesian vectors, summing F1 and F2, and finding the magnitude and direction angles alpha, beta, gamma.

Explore concurrent and coplanar forces in two-dimensional particle equilibrium. Learn to draw and label free body diagrams and apply the x- and y-equilibrium equations.

Master free body diagrams by labeling all forces, including magnitudes and distances, and determine tension or compression directions. Learn equilibrium, components, spring forces, and pulley implications for accurate force analysis.

Draw a free body diagram at point A to identify AB, AC, and 60 N load; use k = 300 N/m and geometry to find AC's unstretched length 0.087 m.

Learn to solve a three-point rope equilibrium problem by drawing free body diagrams for b and c, applying equilibrium equations, and using consistent tension to determine the unknown mass.

Master three-dimensional particle equilibrium by drawing a free-body diagram, applying sum of forces in x, y, z, and resolving cable forces with pythagoras to balance a weight.

Compute position vectors between two points using coordinates, derive unit vectors along a line, and obtain the cartesian force vector by multiplying the unit vector by its magnitude in newtons.

Develop techniques to derive the unit vector of a line-directed force, compute the position vector, and determine B’s x and y coordinates and A’s z from a five-meter rope.

learn to compute dot products of position vectors, project forces along and perpendicular to a line using unit vectors, and extract parallel and perpendicular force components.

apply the dot product to project a 300 newton force along BC, determining the parallel and perpendicular components and using the unit vector along BC.

Explore moments of a force using scalar and cross product methods, define moment about a point as F times the perpendicular distance, and apply anticlockwise positive, clockwise negative.

Calculate the resultant moment of five forces using perpendicular distances and clockwise negative, anticlockwise positive conventions. Break the 7 N force into components and sum moments to determine rotation.

Calculate the moment of a force using the cross product in 2D and 3D with Cartesian vectors. Apply the right-hand rule and r cross f.

Compute the moment about the origin using the cross product of r and F, with r = 1.2 i + 1.2 j and F at 60 degrees, giving M = -492 k N·m.

learn to compute the cross product on a calculator by defining two three-dimensional vectors, then applying the cross product to obtain the moment about a point in newton-meters.

Compute the moment of a force about point b using r_ba cross f, with r_ba = a−b, yielding m = 242 i + 182 j + 94 k N·m.

Learn to compute the moment of a force about an axis using a position vector, the cross product with the force, and the dot product with the axis unit vector.

Compute the moment of a 600 N force about a specified axis using unit vectors, dot product, and cross product to obtain the cartesian force vector.

Explore the moment of a couple, using scalar and vector analysis to compute moments from equal and opposite forces, and identify clockwise negative and anticlockwise positive directions.

Compute the resultant moment from three couples using the perpendicular distances between force lines, sum the moments, and arrive at a final 490 newton-meters clockwise torque.

Compute the moment of a couple via vector analysis by crossing the position vector with the couple force; use any point along the lines of action.

Compute the moment of a couple via the cross product of the position vector and force, using r from B to A to obtain a Cartesian vector moment.

Learn to reduce a force and couple system to a single resultant force and moments about a point using scale analysis or vector analysis, determining magnitude and direction.

This lecture reduces the pipe assembly's forces and moments to a resultant force and a couple of moments at point A, using Cartesian vectors and r × F.

Further simplify a force and couple system on a disk in the x, y and z plane by replacing loading with an equivalent resultant force and its line-of-action coordinates.

Replace the loading system with an equivalent force and determine its line of action coordinates in x, y, and z using vector analysis and moment calculations.

Apply two-dimensional rigid body equilibrium by analyzing cables, pins, rollers, and fixed supports, resolve forces into x and y components, and use sum fx, sum fy, and moments.

Apply free body diagrams and equilibrium equations to determine the horizontal and vertical reactions at supports A and B in a two-dimensional rigid beam, using sums of forces and moments.

Solve rigid body equilibrium in three dimensions by balancing forces and moments for cables, beams, bearings, and pins using X, Y, Z components and three-axis equations.

Identify two force members as equal in magnitude and opposite in direction, then draw free body diagrams and resolve the forces into x and y components and hinge components.

Apply the method of sections to find truss member forces by cutting through the required members with one section, drawing a minimal free body diagram, and solving with equilibrium equations.

Apply the method of sections to a truss example, cutting through members DF, DG, GE, drawing a free body diagram, and solving equilibrium to identify tension or compression.

determine if a member is in tension or compression using a free body diagram, sign conventions, and positive/negative results for forces A, B, and C.

Apply the method of joints to determine forces in a simple truss, using free-body diagrams and equilibrium in x, y, and moments to identify tension or compression.

Learn zero force members in trusses: when two meet with no external load they have zero force, and when three meet with two collinear, the remaining member is zero force.

Identify zero force members in a truss using two scenarios: two members join at a joint with no external load, or external forces render them nonzero.

Explore frames and machines by analyzing joint forces with free body diagrams, applying equal and opposite components, solving with as many equations as unknowns, and using moments about intersection points.

Draw free body diagrams for frames and machines, determine the horizontal and vertical force components at A, B, and C, and use equilibrium and moments to find unknowns.

Define the x and y axes and apply centroid formulas to compute coordinates of a workpiece’s centroid, using areas and positive or negative space for triangles, semicircles, arcs, and shapes.

Calculate the centroid of a composite metal piece by partitioning into rectangles, triangles, and a semicircle, then combine x and y centroids with area weights to locate the overall centroid.

Calculate the centroid of a wire along a circular arc using arc centroid formulas, radians, and coordinate decomposition to determine the wire's x and y centroid.

Compute the resultant of a simple distributed load by using rectangle and triangle areas and centroids, then locate the force on the beam with moments.

Convert a distributed loading into a resultant force by summing areas of triangles and a rectangle, then locate the resultant on the beam using centroids and moment balance.

Explore moments of inertia, the second moment of area, and the parallel axis theorem for calculating axis and centroid-based inertia across circles, rectangles, triangles, and more.

Compute the moment of inertia about the y axis for a rectangle-triangle-hole composite using the parallel axis theorem, summing centroidal inertias with area times distance squared and subtracting the hole.

Learn to compute internal forces in beams using the method of sections, drawing free body diagrams, and applying equilibrium with sign conventions for shear, normal force, and bending moment.

Determine the normal force, shear force, and moment in a structural member by drawing a free body diagram, selecting the right-hand side, and using centroid-based load calculations and reaction analysis.

Draw free body diagrams, compute reactions, and construct shear force diagrams for a beam with a hinge and distributed load to prepare for bending moment diagrams.

Draw the free-body diagram, apply the left-hand section with anticlockwise as positive, and derive the bending moment function M(x) for a beam with distributed loading.